Question

If E and F are events such that \(P(E)=\frac{1}{4},P(F)=\frac{ 1}{2}\) and P(E and F)\(=\frac{1}{8}\), find (i) P(E or F), (ii) P(not E and not F).

Answer 1

Here, \(P(E) =\frac{1}{4} , P(F) =\frac{1}{2}\) , and \(P(E\) and\(F) =\frac{1}{8}\)
 

(i) We know that\(P(E\) or \(F) = P(E) + P(F) - P(E\) and \(F)\)

\(∴P(E\) or \(F) =\frac{1}{4}+\frac{1}{2}-\frac{1}{8}=2+4-\frac{1}{8}=\frac{5}{8}\)

 

(ii) From (i), P(E orF) = P (E U F)\(=\frac{5}{8}\)

We have (EUF)=(E∩F)      [By De Morgans law]

∴P(E∩F)=P(EUF)

Now, P(EUF)=1-P(EUF)\(=1-\frac{5}{8}=\frac{3}{8}\)

∴P(E∩F)\(=\frac{3}{8}\)

Thus, P(not E and not F)\(=\frac{3}{8}\)